If you are willing to cut an opening in the bottom of the cp box, you can put in latches. Then whenever you needed to access to the cp, just reach inside the coin door and up the opening and un-latch.
The high height hinge would work for your round cp. Also, as mention, wood block on all 4 side would be an added bonus.
Velcro, I don't know about other, but my luck with them has not been good epecially with mdf. The 2 side sticks to each other nicely, but when I was using them, they tend to peel off the mdf top whenever I left them. Now, on my heavy 4 player one, I use use them clamp thinge like severdhed mention plus a few magnet ones. On my 2 player one, I use a single latch similar to the picture.